The gluon propagator in Feynman gauge by the method of stationary variance

TL;DR

This paper investigates the low-energy behavior of pure Yang-Mills SU(3) gauge theory in Feynman gauge using a second-order variational method, revealing a finite gluon propagator and a non-vanishing ghost dressing function.

Contribution

It applies the method of stationary variance to derive coupled integral equations for gluon and ghost propagators, providing new insights into their infrared behavior in Feynman gauge.

Findings

Gluon propagator is finite in the infrared with a dynamical mass.

Ghost dressing function remains finite and does not vanish in the infrared.

A decoupling scenario is observed, contrasting some recent results.

Abstract

The low-energy limit of pure Yang-Mills SU(3) gauge theory is studied in Feynman gauge by the method of stationary variance, a genuine second-order variational method that is suited to deal with the minimal coupling of fermions in gauge theories. In terms of standard irreducible graphs, the stationary equations are written as a set of coupled non-linear integral equations for the gluon and ghost propagators. A physically sensible solution is found for any strength of the coupling. The gluon propagator is finite in the infrared, with a dynamical mass that decreases as a power at high energies. At variance with some recent findings in Feynman gauge, the ghost dressing function does not vanish in the infrared limit and a decoupling scenario emerges as recently reported for the Landau gauge.